Ernest D. Courant

The Dynamics of a Synchrotron with Straight Sections

The equations describing the ``betatron and ``synchrotron oscillations of a particle being accelerated in a synchrotron having straight sections are obtained. In particular, the relative increase in the ratio of either betatron‐oscillation frequency to the frequency of revolution is found to be approximately half the ratio of the total length of straight sections to the orbit circumference. The effect of magnetic fringing fields is considered. With regard to the synchrotron phase oscillation, it is found that the criterion of non‐relativistic adiabatic damping is no longer that n exceed ⅔ but that it exceed ⅔ by at least ⅓ of the ratio of the total length of the straight sections to the orbit circumference.

Commissioning and future plans for polarized protons in RHIC

Polarized protons were injected and accelerated in the clockwise ring of RHIC to commission the first full helical Siberian snake ever used in an accelerator. With the snake turned on, the stable spin direction is in the horizontal plane. Vertically polarized protons were injected with the snake off. The snake was adiabatically ramped to give a spin rotation of 180/spl deg/ around a horizontal rotation axis about 13/spl deg/ from the longitudinal. When the beam was accelerated from injection G/spl gamma/ = 46.5 to G/spl gamma/ = 48 the spin flipped sign as expected and polarization was preserved. At G/spl gamma/ = 48 without the snake, no polarization was observed since several spin resonances were crossed. Eventually polarized beam was accelerated to G/spl gamma/ = 55.7 (29.1 GeV). In the next proton running period we plan to run with two full helical snakes in each ring and collide both transversely and longitudinally polarized protons at an energy around 100 GeV per beam.

Revision of Gas Scattering Theory

Previous estimates of the loss of protons through gas scattering are revised to include effects of scattering through angles large enough for immediate particle loss. In multiple‐scattering theory, overestimates of loss may occur through use of the Born approximation. Appropriate corrections are discussed.

Commissioning spin rotators in RHIC

During the summer of 2002, eight superconducting helical spin rotators were installed into RHIC in order to control the polarization directions independently at the STAR and PHENIX experiments. Without the rotators, the orientation of polarization at the interaction points would only be vertical. With four rotators around each of the two experiments, we can rotate either or both beams from vertical into the horizontal plane through the interaction region and then back to vertical on the other side. This allows independent control for each beam with vertical, longitudinal, or radial polarization at the experiment. In this paper, we present results from the first run using the new spin rotators at PHENIX.

FFAG lattice without opposite bends

A future neutrino factory or Muon Collider requires fast muon acceleration before the storage ring. Several alternatives for fast muon acceleration have previously been considered. One of them is the FFAG (Fixed Field Alternating Gradient) synchrotron. The FFAG concept was developed in 1952 by K. R. Symon (ref. 1). The advantages of this design are the fixed magnetic field, large range of particle energy, simple RF; power supplies are simple, and there is no transition energy. But a drawback is that reverse bending magnets are included in the configuration; this increases the size and cost of the ring. Recently some modified FFAG lattice designs have been described where the amount of opposite bending was significantly reduced (ref. 2, ref. 3).

Mass Separation of High Energy Particles in Quadrupole Lens Focusing Systems

In systems for mass separations of high energy particles, the separation achieved depends not only on the applied electric field but also on the characteristics of the systems of magnetic lenses which may be used to contain and focus the beam of particles. Quantitative relations for the mass separation and momentum dispersion are derived. It is shown that systems can be designed involving a module of magnetic lenses and electric field such that, when the module is repeated indefinitely, the mass separations at successive foci increase linearly with the number of modules.

Mapping out the full spin resonance structure of RHIC

We extended the ability of DEPOL to calculate coupled spin resonances and used it to determine the location and strength of both intrinsic and coupled spin resonances in RHIC. In particular we are interested in the full resonance structure with solenoidal elements turned on and with quadrupole rolls.

A comparison of several lattice tools for computation of orbit functions of an accelerator

The values of orbit functions for accelerator lattices as computed with accelerator design programs may differ between different programs. For a simple lattice, consisting of identical constant-gradient bending magnets, the functions (horizontal and vertical betatron tunes, dispersions, closed orbit offsets, orbit lengths, chromaticities etc.) can be evaluated analytically. This lattice was studied with the accelerator physics tools SYNCH [1], COSY INFINITY [2], MAD [3], and TEAPOT [4]. It was found that while all the programs give identical results at the central design momentum, the results differ substantially among the various lattice tools for non-zero momentum deviations. Detailed results and comparisons are presented.

Helical Siberian snakes

Elimination of spin resonances is possible when siberian snakes are used in circular accelerators. Results of analysis and computer calculations of the helical siberian snakes are presented. A single helical snake may be suitable for use in a ring such as the proposed European Hadron Facility.(AIP)

FFAG lattice for muon acceleration with distributed RF

A future muon collider or neutrino factory requires fast acceleration to minimize muon decay. We have previously described an FFAG ring that accelerated muons from 10 to 20 GeV in energy. The ring achieved its large momentum acceptance using a low-emittance lattice with a small dispersion. In this paper, we present an update on that ring. We have used design tools that more accurately represent the rings behavior at large momentum offsets. We have also improved the dynamic aperture from the earlier design.